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Hyperspherical harmonics are extremely useful in nuclear physics
and reactive scattering theory. However, their use has been
confined to specialists with very strong backgrounds in
mathematics. This book aims to change the theory of hyperspherical
harmonics from an esoteric field, mastered by specialists, into an
easily-used tool with a place in the working kit of all theoretical
physicists, theoretical chemists and mathematicians. The theory
presented here is accessible without the knowledge of Lie-groups
and representation theory, and can be understood with an ordinary
knowledge of calculus. The book is accompanied by programs and
exercises designed for teaching and practical use.
In theoretical physics, theoretical chemistry and engineering, one
often wishes to solve partial differential equations subject to a
set of boundary conditions. This gives rise to eigenvalue problems
of which some solutions may be very difficult to find. For example,
the problem of finding eigenfunctions and eigenvalues for the
Hamiltonian of a many-particle system is usually so difficult that
it requires approximate methods, the most common of which is
expansion of the eigenfunctions in terms of basis functions that
obey the boundary conditions of the problem. The computational
effort needed in such problems can be much reduced by making use of
symmetry-adapted basis functions. The conventional method for
generating symmetry-adapted basis sets is through the application
of group theory, but this can be difficult. This book describes an
easier method for generating symmetry-adapted basis sets
automatically with computer techniques. The method has a wide range
of applicability, and can be used to solve difficult eigenvalue
problems in a number of fields. The book is of special interest to
quantum theorists, computer scientists, computational chemists and
applied mathematicians.
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